scholarly journals Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems

2010 ◽  
Vol 32 (6) ◽  
pp. 3228-3250 ◽  
Author(s):  
Jie Shen ◽  
Haijun Yu
Keyword(s):  
Elliptic Problems ◽  
Sparse Grid ◽  
High Dimensional

scholarly journals A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection

2015 ◽  
Vol 53 (3) ◽  
pp. 1508-1536 ◽  
Author(s):  
G. Zhang ◽  
C. Webster ◽  
M. Gunzburger ◽  
J. Burkardt
Keyword(s):  
Grid Method ◽  
Sparse Grid ◽  
High Dimensional ◽  
Discontinuity Detection ◽  
Sparse Grid Method

scholarly journals Parallelisation of sparse grids for large scale data analysis

2006 ◽  
Vol 48 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Jochen Garcke ◽  
Markus Hegland ◽  
Ole Nielsen
Keyword(s):  
Large Scale ◽  
Predictive Modelling ◽  
Sparse Grids ◽  
Sparse Grid ◽  
High Dimensional ◽  
Combination Technique ◽  
Parallel Solvers ◽  
Regular Grids ◽  
Timing Model ◽  
Dimensional Approximation

AbstractSparse grids are the basis for efficient high dimensional approximation and have recently been applied successfully to predictive modelling. They are spanned by a collection of simpler function spaces represented by regular grids. The sparse grid combination technique prescribes how approximations on a collection of anisotropic grids can be combined to approximate high dimensional functions.In this paper we study the parallelisation of fitting data onto a sparse grid. The computation can be done entirely by fitting partial models on a collection of regular grids. This allows parallelism over the collection of grids. In addition, each of the partial grid fits can be parallelised as well, both in the assembly phase, where parallelism is done over the data, and in the solution stage using traditional parallel solvers for the resulting PDEs. Using a simple timing model we confirm that the most effective methods are obtained when both types of parallelism are used.

scholarly journals A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection

2014 ◽  
Author(s):  
Guannan Zhang ◽  
Clayton G. Webster ◽  
Max D. Gunzburger ◽  
John V. Burkardt
Keyword(s):  
Grid Method ◽  
Sparse Grid ◽  
High Dimensional ◽  
Discontinuity Detection ◽  
Sparse Grid Method
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